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Area problemCalculate the area of the region enclosed by the x-axis and one arch of the...

portoruj | Student, Grade 10 | eNoter

Posted June 3, 2011 at 10:04 PM via web

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Area problem

Calculate the area of the region enclosed by the x-axis and one arch of the curve y=sin x.

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giorgiana1976 | College Teacher | Valedictorian

Posted June 4, 2011 at 3:26 AM (Answer #2)

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The area bounded by the curve y = sin x and x axis is the definite integral of the given function.

Since the boundary lines are not given, we'll suppose that x = -pi/2 and x = pi/2.

Int sin x dx = -cos x

We'll apply Leibniz Newton formula:

Int sin x dx = F(b) - F(a)

a = -pi/2 and b = pi/2Since the sine function is odd, we'll consider the integral as:

Int sin x dx = 2 Int sin x dx from x = 0 to x = pi/2.

2Int sin x dx = 2[-cos (pi/2) + cos 0]

2Int sin x dx = 2(0 + 1)

2Int sin x dx = 2

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